Rebuilding checkbox indicators as in quick favourites
Feeling qualified to answer this by myself:

Inside the draw() method of the menu class, the self.layout.prop() method can to be used to access a property and automatically draw the desired checkbox:

class MyMenu(bpy.types.Menu):

    bl_idname = "OBJECT_MT_my_menu" 
    bl_label = "My Menu"

    def draw(self, context):
        self.layout.prop(view3d_overlay, "show_bones", text="Toggle Bones")